I am betting that it was because it wasn't written specifically for the film.
Oscar rules state that any piece of music is ruled ineligible if it receives commercial release prior to use in the film; hence why Jonny Greenwood's masterful score for "There Will Be Blood" was given the shaft back in '08...
Actually, my understanding is that it is considered ineligible for not being featured audibly enough in the film. Too low in the driving scene and too late in the end credits.
In any case people don't think about best song much for movie awards, myself included. I think of OKOL from NPP myself and not the film.
It's good to see that L&M does keep popping up in various awards circles and in several instances It's been in the top 5 films of the year for one category or another. Nice that some critics and insiders actually saw it and did their homework. Is L&M the best film of the year.....maybe not, but it sure is worthy of award nominations....including best picture.